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Preprint (Author's original)arXiv.org - Non-exclusive license to distribute, Open
Preprint
m-structures determine integral homotopy type
26 Sep 1998
Abstract
This paper proves that the functor $C(*)$ that sends pointed,
simply-connected CW-complexes to their chain-complexes equipped with diagonals
and iterated higher diagonals, determines their integral homotopy type --- even
inducing an equivalence of categories between the category of CW-complexes up
to homotopy equivalence and a certain category of chain-complexes equipped with
higher diagonals. Consequently, $C(*)$ is an algebraic model for integral
homotopy types similar to Quillen's model of rational homotopy types. For
finite CW complexes, our model is finitely generated. Our result implies that
the geometrically induced diagonal map with all ``higher diagonal'' maps (like
those used to define Steenrod operations) collectively determine integral
homotopy type.
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Details
- Title
- m-structures determine integral homotopy type
- Creators
- Justin R Smith
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- [Retired Faculty]
- Other Identifier
- 991021880184404721